The flexibility of microwave photonics provides advantages over electronic circuitry, yet the lack of integrated chip-scale devices limits its practical application. This study presents microwave filters based on photonic crystal waveguides with controllable delays as a step towards intregable circuits.

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Integrable microwave filter based on a photonic crystal delay line

We experimentally investigate four-wave mixing (FWM) in short (80 μm) dispersion-engineered slow light silicon photonic crystal waveguides. The pump, probe and idler signals all lie in a 14 nm wide low dispersion region with a near-constant group velocity of c/30. We measure an instantaneous conversion efficiency of up to −9dB between the idler and the continuous-wave probe, with 1W peak pump power and 6nm pump-probe detuning. This conversion efficiency is found to be considerably higher (>10 × ) than that of a Si nanowire with a group velocity ten times larger. In addition, we estimate the FWM bandwidth to be at least that of the flat band slow light window. These results, supported by numerical simulations, emphasize the importance of engineering the dispersion of PhC waveguides to exploit the slow light enhancement of FWM efficiency, even for short device lengths.

Four-wave mixing in slow light engineered silicon photonic crystal waveguides

There are two standard methods for controlling the group velocity of light. One makes use of the dispersive properties associated with the resonance structure of a material medium. The other makes use of structural resonances, such as those that occur in photonic crystals. Both procedures have proved useful in a variety of situations. In this work we contrast these two approaches, especially in terms of issues such as the kinematics of energy flow though the system and the resulting implications for the behavior of nonlinear optical processes in these situations. Stated differently, this paper addresses the question of when nonlinear optical processes are enhanced through use of slow-light interactions and when they are not.

Material slow light and structural slow light: similarities and differences for nonlinear optics [Invited]

We review recent advances related to slow light in periodic structures, where the refractive index varies along one or two directions, i.e. gratings and planar photonic crystals. We focus on how these geometries are conducive to enhancing the nonlinear interaction between light and matter. We describe the underlying theory developed for shallow gratings, but whose conclusions can be extended to planar photonic crystal waveguides, in particular the enhancement of third-order nonlinear processes with slow light. We review some experiments showing how gratings have been used for pulse compression and the generation of slow gap solitons. We then present recent nonlinear experiments performed in photonic crystal waveguides that demonstrate the strong reinforcement of nonlinear third-order optical phenomena with slow light. We discuss the challenges associated with slow light in these 2D structures and their unique advantage—dispersion engineering—for creating broadband nonlinear devices for all-optical signal processing. By breaking down the relation between dispersion and group velocity imposed in gratings, these structures also offer new opportunities for generating soliton-like effects over short length scales, at low powers and with short pulses.

http://iopscience.iop.org/article/10.1088/2040-8978/12/10/104003/pdf

Slow light enhanced nonlinear optics in periodic structures

We demonstrate experimentally that the fiber to fiber total insertion loss into a single-mode waveguide in a suspended photonic crystal membrane can be reduced to less than 10 dB (input, output, and propagation) without introducing any supplementary processing step (e.g., polymer deposition and etching). This is achieved through a suitable design of the waveguide end-facets minimizing the impedance mismatch and thereby the residual reflectance at the waveguide ends.

Photonic crystal membrane waveguides with low insertion losses

We report highly efficient four wave mixing in a GaInP photonic crystal waveguide. Owing to its large bandgap, the ultrafast Kerr nonlinearity of GaInP is not diminished by two photon absorption and related carrier effects for photons in the 1550 nm range. A four-wave-mixing efficiency of -49 dB was demonstrated for cw pump and probe signals in the milliwatt range, while for pulsed pumps with a peak power of 25 mW the conversion efficiency increased to -36 dB. Measured conversion efficiency dependencies on pump probe detuning and on pump power are in excellent agreement with a simple analytical model from which the nonlinear parameter gamma is extracted. Gamma scales approximately with the square of the slow down factor and varies from 800 W(-1) m(-1) at a pump wavelength lambda(p)=1532 nm to 2900 W(-1) m(-1) at lambda(p)=1550 nm. These values are consistent with those obtained from self phase modulation experiments in similar devices.

Highly efficient four wave mixing in GaInP photonic crystal waveguides.

The equations for Four-Wave-Mixing in a photonic crystal waveguide are derived accurately in the hypotesis of negligible nonlinear absorption. The dispersive nature of slow-light enhancement, the impact of Bloch mode reshaping in the nonlinear overlap integrals and the tensor nature of the third order polarization are therefore taken into account. Numerical calculations reveal substantial differences from simpler models, which increase with decreasing group velocity. We predict that the gain for a 1.3 mm long, un-optimized GaInP waveguide will exceed 10 dB if the pump power exceeds 1 W.

Theory of slow light enhanced four-wave mixing in photonic crystal waveguides.

The equations for Four-Wave-Mixing in a Photonic Crystal waveguide are derived accurately. The dispersive nature of slow-light enhancement, the impact of Bloch mode reshaping in the nonlinear overlap integrals and the tensor nature of the third order polarization are therefore taken into account. Numerical calculations reveal substantial differences with simpler models, which increase with decreasing group velocity. We predict that the gain for a 1.3 mm long, unoptimized GaInP waveguide will exceed 10 dB if the pump power exceeds 1 W.

Theory of Slow Light Enhanced Four-Wave Mixing in Photonic Crystal Waveguides

We investigate the impact of disorder on the propagation of photonic crystal waveguide modes using phase-sensitive optical low-coherence reflectometry.Combined with a suitable numerical processing, this technique reveals a considerable amount of information that we cast as time-wavelength reflectance maps. By comparing measurements on different samples, we easily identify inter-mode scattering and propagation losses mediated by slow leaky modes. We also characterize the dispersive behaviour of point defects. Our results verify previous theoretical predictions about the general group velocity scaling of losses and the dominant role of backscattering.

Time-Wavelength Reflectance Maps of Photonic Crystal Waveguides: A New View on Disorder-Induced Scattering

The nonlinear effective coefficients of self-, cross-phase modulation and four-wave mixing are rigorously derived for photonic crystal waveguides. The enhancement of nonlinearities in the regime of slow light is determined.

G. Vadala

Papers

Highly efficient four wave mixing in GaInP photonic crystal waveguides.

Theory of slow light enhanced four-wave mixing in photonic crystal waveguides.

Theory of Slow Light Enhanced Four-Wave Mixing in Photonic Crystal Waveguides

Time-Wavelength Reflectance Maps of Photonic Crystal Waveguides: A New View on Disorder-Induced Scattering

Slow light enhancement of nonlinear effects in photonic crystal waveguides